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Rings with Elementary Reduction of Matrices

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Ukrainian Mathematical Journal Aims and scope

Abstract

We establish necessary and sufficient conditions under which a quasi-Euclidean ring coincides with a ring with elementary reduction of matrices. We prove that a semilocal Bézout ring is a ring with elementary reduction of matrices and show that a 2-stage Euclidean domain is also a ring with elementary reduction of matrices. We formulate and prove a criterion for the existence of solutions of a matrix equation of a special type and write these solutions in an explicit form.

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Authors and Affiliations

  1. Lviv University, Lviv

    B. V. Zabavskii & O. M. Romaniv

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  1. B. V. Zabavskii
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  2. O. M. Romaniv
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Zabavskii, B.V., Romaniv, O.M. Rings with Elementary Reduction of Matrices. Ukrainian Mathematical Journal 52, 1872–1881 (2000). https://doi.org/10.1023/A:1010403909652

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  • DOI: https://doi.org/10.1023/A:1010403909652

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